The female had crawled into the wheel arch of the vehicle while it was parked in the hills near the city of Adelaide last weekend.
The driver was only alerted to the marsupial's presence when he stopped and heard her traumatised cries.
Rescuers eventually came to take the wheel off and free the koala.
"I could smell her burnt fur," Jane Brister from the Fauna Rescue charity told Reuters news agency.
After a few days of resting and feeding in captivity, the animal was released into the forest.
Koalas are native to Australia and classified as a "vulnerable" species. There are fewer than 100,000 left in the wild, according to the Australian Koala Foundation.